As an attractive enabling technology for next-generation wireless communications, network slicing supports diverse customized services in the global space-air-ground integrated network (SAGIN) with diverse resource constraints. In this paper, we dynamically consider three typical classes of radio access network (RAN) slices, namely high-throughput slices, low-delay slices and wide-coverage slices, under the same underlying physical SAGIN. The throughput, the service delay and the coverage area of these three classes of RAN slices are jointly optimized in a non-scalar form by considering the distinct channel features and service advantages of the terrestrial, aerial and satellite components of SAGINs. A joint central and distributed multi-agent deep deterministic policy gradient (CDMADDPG) algorithm is proposed for solving the above problem to obtain the Pareto optimal solutions. The algorithm first determines the optimal virtual unmanned aerial vehicle (vUAV) positions and the inter-slice sub-channel and power sharing by relying on a centralized unit. Then it optimizes the intra-slice sub-channel and power allocation, and the virtual base station (vBS)/vUAV/virtual low earth orbit (vLEO) satellite deployment in support of three classes of slices by three separate distributed units. Simulation results verify that the proposed method approaches the Pareto-optimal exploitation of multiple RAN slices, and outperforms the benchmarkers.
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